I use a little yard called A J Ferguson (clicky) between Shepherd's Bush and Acton - there's a few other yards around, but Ferguson's are literally 5 minutes away from me so no contest really, unless you're after something they don't usually stock. I had quite a bit of Red Cedar last year for a bike / garden store I built for a customer and Champion were a lot cheaper for that, but for most things Ferguson's are well stocked, convenient, and very helpful.
I bought a single sheet of 12mm birch ply from Creffields in Tilehurst, Berkshire (www.creffields.co.uk) for £25 cash. They are very friendly but not much used to customers turning up and collecting so the guy just took the took the money and put it straight in the staff Christmas party tin! Their main business is sheets and sheets of material for shopfitting and film sets.